A chordal graph has a dominating clique iff it has diameter at most 3. A strongly chordal graph which has a dominating clique has one as small as the smallest dominating set-and, furthermore, there is a linear-time algorithm to find such a small dominating clique.
Packingr-Cliques in Weighted Chordal Graphs
โ Scribed by P. Hell; S. Klein; L. T. Nogueira; F. Protti
- Book ID
- 106344181
- Publisher
- Springer US
- Year
- 2005
- Tongue
- English
- Weight
- 160 KB
- Volume
- 138
- Category
- Article
- ISSN
- 0254-5330
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๐ SIMILAR VOLUMES
## Abstract We study the squares and the clique graphs of chordal graphs and various special classes of chordal graphs. Chordality conditions for squares and clique graphs are given. Several theorems concering chordal graphs are generalized. ยฉ 1996 John Wiley & Sons, Inc.
We study two new special families of complete subgraphs of a graph. For chordal graphs, one of these reduces to the family of minimal vertex separators while the other is empty. When the intersection characterization of chordal graphs is extended from acyclic (i.e., K3-free chordal) hosts to K4-free
## Abstract The clique graph __K__(__G__) of a graph is the intersection graph of maximal cliques of __G.__ The iterated clique graph __K__^__n__^(__G__) is inductively defined as __K__(K^nโ1^(__G__)) and __K__^1^(__G__) = __K__(__G__). Let the diameter diam(__G__) be the greatest distance between